A gauge theory for the quantum planar three-body problem

DOI10.1063/1.527588zbMath0625.53062OpenAlexW2056008105MaRDI QIDQ3027863

Toshihiro Iwai

Publication date: 1987

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527588

zbMATH Keywords

rotationgauge theoryvibrationcenter-of-mass systemconnection theory due to Guichardetnonrigidity of moleculesplanar triatomic molecules

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Applications of global differential geometry to the sciences (53C80) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Connections (general theory) (53C05)

Related Items (21)

Shape dynamics of N point vortices on the sphere ⋮ SO(4) algebraic approach to the three-body bound state problem in two dimensions ⋮ Permutation-symmetric three-particle hyper-spherical harmonics based on the \(\operatorname{S}_{3}\otimes\operatorname{SO}(3)_{rot} \subset \operatorname{O}(2)\otimes\operatorname{SO}(3)_{ rot} \subset \operatorname{U}(3) \rtimes \operatorname{S}_{2} \subset \operatorname{O}(6)\) subgroup chain ⋮ The reduction of a quantum system of three identical particles on a plane ⋮ Reduction of quantum systems with symmetry, continuous and discrete ⋮ Two classes of dynamical systems all of whose bounded trajectories are closed ⋮ An integrable model of a planar tri-atomic molecule ⋮ The irreducible tensor approach in the separation of collective angles in the quantum \(N\)-body problem ⋮ Isoholonomic problems and some applications ⋮ Reduction of quantum systems on Riemannian manifolds with symmetry and application to molecular mechanics ⋮ A geometric setting for the quantum planar n-body system, and a U(n−1) basis for the internal states ⋮ \(\mathrm{O}(6)\) algebraic approach to three bound identical particles in the hyperspherical adiabatic representation ⋮ Unnamed Item ⋮ Classical and quantum mechanics of jointed rigid bodies with vanishing total angular momentum ⋮ Total S-matrix and adiabatic amplitudes for the three-body problem ⋮ Symplectic reduction and the Lie–Poisson shape dynamics of N point vortices on the plane ⋮ Rotational-vibrational energy spectra of triatomic molecules near relative equilibria ⋮ Differential geometry of collective models ⋮ Geometric mechanics of many-body systems ⋮ Connections and effective S-matrix in triangle representation for quantum scattering ⋮ Unnamed Item

Cites Work

• Unnamed Item
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• The four-dimensional conformal Kepler problem reduces to the three-dimensional Kepler problem with a centrifugal potential and Dirac’s monopole field. Classical theory
• Quantization of the conformal Kepler problem and its application to the hydrogen atom
• A Symmetric Representation for Three-Body Problems. I. Motion in a Plane

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